Neural Networks Controler of a Lower Limbs Robotic Rehabilitation

Chair

M. A. Mamou and N. Saadia

Institute of Electronic, USTHB University, Bab-Ezzouar, Algiers, Algeria

Keywords: Feed Forward Neural Network, PID Controler, Kinematic Model, Path Tracking, Rehabilitation Robot,

Lower Limbs.

Abstract: In this paper, we propose a new control law using a kinematic model based on a Feed forward neural

network (FFNN). This controller is designed for the control of a robotic rehabilitation chair of the lower

limbs designed and created in the LRPE laboratory, with high accuracy. The results of the validation tests,

show that the lower limb joints trajectories of the proposed control law are similar to the physiological joints

trajectories of a patient. This demonstrates that the proposed control law provides a high performance and a

fast convergence with extremely low error.

1 INTRODUCTION

Robotic devices find a growing interest in their use

to assist in providing therapy rehabilitation

following neurological injuries such as spinal cord

injury, stroke and after a joint and / or muscle

traumas (Reinkensmeyer, 2004; Riener, 2005).

Many rehabilitation devices of human limbs and

joints are the subject of study by researchers to assist

therapists and patients. In this context, we developed

in the LRPE laboratory a rehabilitation prototype of

lower limbs. The device is a robotic chair for

neuromatrix rehabilitation of lower limb with two

motorized orthotics (right and left leg), with 3DOF

for each of them (hip, knee and ankle). Position

sensors are mounted on each link to manage the flow

of a predetermined motion in real time.

We find in literature different strategies to

control the path to follow for robotic rehabilitation.

For the upper limbs, (Lo, 2012) reviews the control

strategies, among the control structures, devices

using PID (Moughamir, 05), others use either fuzzy

or neuro-fuzzy logic (Zeinali, 2010; Rahman, 2006).

However, for lower limb, there are not many works

addressing control strategy to control desired

trajectories. Schmitt & Métrailler used to control

Motion Maker in (Schmitt, 2004) an intelligent

central unit "Control unit", called Industrial PC,

composed of different modules; (Seddiki, 2006)

proposed three control laws for a SOKINETICS’s

good trajectory tracking, two with a PI and a third

fuzzy H-infinite hybrid control. Fuzzy logic has

been used in (Akdogan, 2011). The control in,

(Anama, 2012) is done with a PID. Meanwhile, they

used a hierarchical control with PD, even modified

genetic algorithms have been used (Jamwal, 2009).

Therefore, we conclude that the use of neural

networks for system control of the lower limbs is not

common.

Our work consists of controlling the trajectory of

a rehabilitation system of lower limbs (robotic

rehabilitation chair, and the originality lies in the

fact that we us the kinematic model of the robotic

rehabilitation chair based on neural networks {Feed

forward neural network (FFNN)}. In this approach a

PID controller is used offline to train the FFNN.

This results in better online results than when using

traditional PID controllers.

The outline of this paper is as follows: First, we

present the rehabilitation system developed in the

LRPE laboratory for which we establish the

geometric and kinematic model before proposing its

control law. Then, we present the control system

used for parameters identification based on a

conventional PID and the new scheme using a neural

controller (feed forward neural network (FFNN)).

After that, we present the implementation of the

controller on the system. Finally, a discussion of the

results and conclusions are presented.

65

A. Mamou M. and Saadia N..

Neural Networks Controler of a Lower Limbs Robotic Rehabilitation Chair.

DOI: 10.5220/0004700700650071

In Proceedings of the International Conference on Biomedical Electronics and Devices (BIODEVICES-2014), pages 65-71

ISBN: 978-989-758-013-0

Copyright

c

2014 SCITEPRESS (Science and Technology Publications, Lda.)

2 SYSTEM DESCRIPTION

The prototype dedicated to the rehabilitation of

lower limbs for patients with motor deficiencies

developed in our laboratory is shown in (figure-1).

The main use of this prototype is to provide

functional rehabilitation of the lower limbs using

functional orthotics. The implemented system allows

the reproduction of physiological joints trajectories

and take back segmental loads of body movements,

especially walking.

Figure 1: Lower limbs rehabilitation chair robot.

The robotic rehabilitation chair is made up of

two orthosis and a seat mounted on a frame. Both

mechanical orthotics, are placed on either side of the

seat. Each orthotic, which can operate around three

degrees of freedom, consists of three joints: hip,

knee and ankle and three segments: thigh, leg and

foot. Joints ensure transmission of movement

between the different segments taking into account

the factor of safety, the patient’s weight and waist

using a mechanism consisting of rods, gears and DC

motors (Merrouche, 2011; Saadia, 2009).

3 SYSTEM MODEL

In order to create the geometric model of the system,

we usual introduce a fixed coordinate system

(frame) in which all objects is referenced. In our

approach, we establish the basic coordinate system

with chair’s frame, represented by Ox

1

y

1

, as shown

in Figure 2. The coordinates of the point are given

according to the plan Ox

2

y

2

which Ox

2

superimposed on l

1

. In the same way, the

coordinates of the last point are given on the plan

Ox

3

y

3

where Ox

3

is superimposed on l

2

.The tool’s

coordinates are expressed in this coordinate system

(Spong, 2005; Fu, 1987). l

1

, l

2

and l

3

represent the

length of each segment,

is the angle between Ox

i

and l

i

.

Figure 2: Three link Coordinate system of the chair’s

frame.

The direct geometric model (DGM) of the system is

represented by the relation

(1)

Where is the vector of joint coordinates such as :

T

(2)

The vector is defined by the elements of the

homogeneous transformation matrix

α

A

β

(Khalil,

2010; Dombre, 2007). This matrix (

α

A

β

) gives the

coordinate frame R

β

from those of frame R

α

:

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

66

0

0

0

00

00

10

01

3

1

0

0

00

00

10

01

4

2

0

0

00

00

10

01

5

,

and

are the lengths corresponding to the

thigh, leg and foot. They can be manually adjusted.

In our test, we choose respectively the values 50, 60

and 25 cm.

We calculate the

0

A

3

matrix which leads to the

coordinate frame R

3

from those of frame R

0

0

0

∗

1

∗

2

0

0

0

0 0

0 0

1 0

0 1

6

Where:

cos

;

;

cos

;

;

cos

;

;

3.1 Kinematic Model

The direct kinematic model (DKM) is given by

(Jazar, 2010; Khalil, 2004):

xtJ

θ

∗

θ

t

(7)

Where J(θ) denotes the (i x j) Jacobian matrix. The

élément «J_ij (θ) » is given by equation (8):

J

θ

δ

f

θ

θ

(8)

The inverse kinematic model (IKM) is calculated

from the inverse matrix J

-1

according to the

mathematical formulas, the model equation is:

θ

tJ

θ

∗xt

(9)

The workspace and manipulability are based on

kinematics criteria often used for robot architecture

selection (Bhangale, 2004). The workspace for one

orthesis of the lower limbs robotic rehabilitation

chair is illustrated in figure-3. This figure shows all

the possible position configurations during the

movement of the joint depending on the previous

one; they are represented by discontinuous lines. As

an example we took a configuration that we have

shown with continuous lines.

Figure 3: One orthesis Workspace.

4 THE CONTROL STRATEGY

In order to control this system, we propose a control

structure using a kinematic model of the robotic

rehabilitation chair based on neural networks (Feed

Forward Neural Network (FFNN)). The control law

is implemented in two steps, the first one is an

offline phase and consists of training the FFNN and

the second law is performed online in order to adjust

the parameters of the FFNN to get the best

parameters of the control structure connected to the

learning.

Given that the two orthesis are identical, they are

represented with the same model equations. For

simplicity reasons, we will command only the right

orthotic. In addition, we use a decoupled architecture

where each joint is controlled separately. Therefore,

we will have three identical control schemes for

each orthotic. The control schemes are illustrated in

(figure 4 -5).

In the first step, to perform the learning

process, we choose to use a PID

controller.

The FFNN controller is trained off-line

through a classical control (PID) law (Figure-

4). The PID is used to identify and provide

the required training data. To train the

FFNNC we use the backpropagation

algorithms.

NeuralNetworksControlerofaLowerLimbsRoboticRehabilitationChair

67

Figure 4: Parameters identification of the control law

structure.

In the second step an online adaptation of the

neural controller to regulate its parameters

according to the task performed is used

(Figure-5).

Figure 5: Real time control law Structure.

The figure below represents the architecture used in

the FFNN. It is composed of three layers. The input

layer consists of three neurons, the hidden layer of

four neurons, and the output layer of one neuron.

Figure 6: Neural network Structure.

The input "E" and output "U" represent the error and

the control vectors respectively. The matrix output

« V » of the hidden layer and the output « U » of the

network are given by:

(10)

(11)

Where (

,

) and (

,

) are the weights and

bias matrices of respectively to adjust. And

0,…,3 number of joints. .and

.

are the

activation function of the neurons in hidden and

output layer. These functions are choose as

sinusoidal for the hidden layer, and as linear for the

neurons of the output layer.

The proposed control law, according to the

equations (12) (Khalil, 2004; Corke, 2011), allows

the matching of error values (Δθ) and the signal

control given by:

(12)

Where:

θ

and θ

are the desired and measured values.

C is the control law.

U is the signal control

Implementation of this control law requires steps

mentioned above and illustrated in ( Figure-4 & 5).

5 IMPLEMENTATION AND

TESTS

To validate the command structure that we have

established, we must make the implementation of

the lower limbs robotic rehabilitation chair by

generating a specified path of the rehabilitation. This

trajectory is a challenge that is the subject of

discussion within the scientific community. Marchal

has made a detailed study that includes several

works on this subject (Marchal-Crespo, 2009). In

this article, we simulate joints trajectory by

generating sinusoidal signals because they are

similar to physiological movements (flexion –

extension). Indeed, it is important to test the

controller with a signal that is as natural as possible

for even of the system behavior. The signal is within

the operating range of the rehabilitation robot.

The architecture of the neural networks used is

made of three layers. The input layer has three

neurons; the hidden layer has four neurons and the

output layer has one neurons.

For the learning function algorithm of the FFNN,

we use the « trainlm » function from the MATLAB

toolbox. Indeed, the network learning function

updates weight and bias values according to the

Levenberg-Marquardt optimization scheme.

« trainlm » is often the fastest backpropagation

algorithm in the toolbox, and is highly

recommended as a first-choice supervised algorithm,

although it requires more memory than other

algorithms (Mathworks). The Neural network’s

parameters (weights and biases) obtained after the

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

68

learning process are given below:

The controller’s parameters of the first joint

3.3668 11.6782 1.8655

7.3454 11.4598 3.7226

3.2088 9.5054 1.7756

10.4749 0.0577 208.5848

;

18.2953

18.7634

20.3442

1.4435

;

10

∗

0.0094 0.0161 0.6235 1.5369

;

619.8668

;

The controller’s parameters of second joint

3.3668 11.6779 1.8655

7.3454 11.4584 3.7226

3.2088 9.5039 1.7756

18.8783 0.1021 376.9088

;

18.2971

18.7659

20.3515

0.4344

;

10

∗

0.0094 0.0161 0.3429 1.7353

;

The controller’s parameters of third joint

6.9021 2.2635 1.7780

10.1509 0.6958 246.7756

24.8331 0.7387 66.6627

10.4108 0.3036 25.4001

;

16.6639

0.1546

3.1295

1.1637

;

∗

0.0286 0.3671 0.5476 1.5733

;

504.9972

;

We present in figure (7) the behavior of the

controller and in figure (8) the evolution of the error

for the three joints (hip, knee and ankle). The

variation of the rehabilitation chair first joint (hip) in

its trajectory is shown in (Figure-7). Figure 8

illustrates the error between the desired and

measured value.

Figure 7: Varying the path of the first joint (hip joint).

Figure 8: The error in the desired trajectory of the first

joint (hip joint).

We generate desired positions joint in the

operating range of the hip joint of the rehabilitation

device, the signal varies between 0° and 40° and as a

starting point 0°. The output obtained (real position

joint) are identical with the signal desired, which

gave an error not exceeding 0.17°.

Figures (9, 10) represent respectively the

variation of the second joint (knee) and its error.

Figure 9: Varying the path of the second joint (Knee

joint).

Figure-10: The error in the desired trajectory of the second

joint (Knee joint).

For the knee joint, the signal is also sinusoidal

shape varying between -30° and -90°, as a starting

point -50°, this range was chosen based on the

operating range of rehabilitation device. The output

signal is obtained similar to the desired signal, the

highest value of the error obtained is 0.1°. The

NeuralNetworksControlerofaLowerLimbsRoboticRehabilitationChair

69

starting point we got an error of 10°, this is due to

the initial position of the joint.

At the end, the variation of the ankle joint and

it’s error are illustrated in (Figures 11 and 12).

Figure 11: Varying the path of the third joint (Ankel joint).

Figure 12: The error in the desired trajectory of the third

joint (Ankel joint).

For the ankle joint, the signal that we generated

varies between 80° and 100°, with 90° initial value.

The output signal is virtually identical to the desired

signal; as a result we had a very weak error, less

than 0.02°.

The plots show that the obtained results are very

good, as the measured values are very close to the

desired ones. In fact, the error’s values does not

exceed (0.2°) most. Nevertheless, the error signals

present considerable oscillation cycle.

Corresponding control signal of the three joints

are shown in Figures (13, 14 and 15)

Figure 13: Control signal (U) of the first joint (hip joint).

Figure 14: Control signal (U) of the second joint (Knee

joint).

Figure 15: Control signal (U) of the third joint (Ankel

joint).

The variation of the amplitude of the control

signal of the three joints is not very intense, we

believe that it is optimal signals, which gave good

performance in the trajectory tracking with very low

error.

6 DISCUSSION AND

CONCLUSIONS

The objective of this work is to establish an

intelligent control law using neural networks for the

kinematic model of the robotic rehabilitation chair of

the lower limbs. This is latter consists of two

orthesis operating in three degrees of freedom. The

implementation of the control law is performed by

generating a similar signal (closer) to the

physiological joint trajectories. To obtain the

smallest possible error and try to get a signal error

with the least possible oscillations, we performed

several learning attempts, with a more or-less long

time. A high frequency of oscillation of the error

signal involves a large variation in the control signal,

which is harmful for the electronic components,

such as motors. However, once this step is done, the

controller performs very well. The implemented

control law gives very good performance. Indeed the

BIODEVICES2014-InternationalConferenceonBiomedicalElectronicsandDevices

70

error of each joint is very small; it does not exceed

(0.2 °). The results are satisfying. However, the error

form of each joint signal has thousands of

oscillations. These oscillations are due to variations

in the successive orders. By varying the desired

signal very quickly, the controller will not be able to

follow; it will give a very big order which leaves the

workspace of the chair. Perspectives, The patient's

weight which varies from one individual to another,

can be regarded as a parameter. Than considered as

an extrinsic disturbance. We propose to improve the

monitoring of the path by using a dynamic model of

the robot in order to take into account all the

parameters and to achieve high accuracy and

minimized oscillations on the output signal.

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